"Versus" is a Latin term that means "against."
In the context of the law, there are at least two parties in a lawsuit who are "against" each other. For this reason, lawsuits are commonly named "party A. versus party B." This lets everyone involved know that the two parties are against each other in the lawsuit.
Versus is commonly abbreviated as "vs." or "v." All variations of the word mean the same thing.
Lawsuits often involve many different types of plaintiffs and defendants. Private citizens, companies and even government bodies, or states, can all be plaintiffs or defendants. So, for example, "versus" may be in used in a lawsuit title such as "The People of the State of California Versus Orenthal James Simpson."
When this word is used in a lawsuit title, it means that one of the parties is taking legal action against the other.